Student-Centered Learning Strategies for Math and Other Subjects

Editor's Note: Paul Bogdan was once an old-fashioned lecturing teacher centered secondary math teacher who left teaching for 14 years to build computer systems. He has come back and is reborn as a student-centered teacher trying to make a difference and trying to figure out what works in today's classroom.

Have you ever taught a lesson and then gave a quiz only to find that very few students have a clue about what you were teaching? What can we do about students who aren't getting it? How can we help the students learn rather than try to teach them? I'm thankful for the opportunity to share some of my ideas and can't wait to hear what you think. Please share your thoughts in the comments section below.

Strategy One: Write detailed lesson plans and give them to the students to execute

In the past I never understood the point of writing lesson plans. I knew my subject matter thoroughly and completely. I felt that all I needed to do was stand up in front of the class and impart my knowledge; and I expected the students to soak it up. Now, I write very detailed lesson plans, but I write them for and give them to the students.

The following is a lesson plan that I give to the students to execute. It covers one section of the Geometry textbook (high school).

Project 2C (Classwork) Congruence and Triangles (4.2) (Page 202)

1. Three vocabulary. Corresponding Angles, Corresponding Sides, Triangle Congruence Statement Write and learn the definitions, include examples, underline, highlight, or change the color of the term. Learn and understand them.

A triangle congruence statement names the two triangles congruent with corresponding angles in corresponding positions in the triangle name. For example: When you write ?ABC??PQR you also mean that ?A??P,?B??Q, and ?C??R. If this is not true, then the congruence statement is false.

Note: Congruent is the same as equal except in math only figures are congruent and only numbers are equal (previously covered).

2. DFU Example: 1. Naming Congruent Pairs (DFU means Done For You.) Copy the question. Copy or write the solution in your own words. Include what you think is important when the instructions are to completely show your work. Be sure to learn what you are doing.

3. UDO Example: Page 205 Guided Practice #1 (UDO means You Do.) This is very similar to DFU Example 1. You must write the question and completely show your work.

Note: When working with congruent figures it helps a lot to draw them both facing the same way. Sometimes you only need to rotate one of them, but sometimes you need to flip one of them over and rotate it. This makes it easy to see corresponding sides and angles. It is easy to do and always makes the problem easier; it often changes a difficult problem into an easy one.

4. DFU Example: 2 (a, b). Using Properties of Congruent Figures

5. UDO Example: Page 205 Guided Practice #4 - 9

6. One theorem. Theorem 4.3 Third Angle Theorem

7. DFU Example: 3. Using the Third Angle Theorem

8. UDO Example: Page 809 Guided Practice #11

9. DFU Example: 4. Determining Whether Triangles are Congruent

10. UDO Example: Page 206 Guided Practice #17

11. DFU Example: 5. Proving Two Triangles are Congruent

12. UDO Example: Page 208 Guided Practice #35

13. One theorem. Theorem 4.4 Properties of Congruent Triangles

The plan guides the students to learn vocabulary, copy and learn examples, and do examples on their own. They need help at first, but soon learn how to teach themselves. Their work is collaborative; they rely on each other for help. They rely on me too, often asking questions. The book weaves the vocabulary into the examples. The book is very thorough, covering all aspects of the standards with very creative examples. Mostly I do one-on-one instruction. My role in the classroom has changed from "imparter of knowledge," to "facilitator of learning." The student centered lesson frees me up to roam about the room and become a resource for explaining, demonstrating, and clarifying precisely those areas each student needs. The students now ask me, instead of me demanding they "listen and learn." When several students are not getting it however, or are making the same mistakes, I will interrupt the class as a whole to explain something of general interest. Those students who want to learn the material excel using this method. It's all about motivation.

Strategy Two: Teach good note-taking skills

Besides learning subject matter, it is essential for students to be taught how to learn. Specific techniques for old fashion note taking are essential. Most textbooks (especially in Science and Social Studies) have pages of narrative followed by questions. Have the student write p1pa1 in the left margin of their paper. This means, page 1 paragraph 1. The student reads the paragraph, writes a short something, and then writes p1pa2. They read, they write, they read, they write, and so forth, until they get to the questions. The students will be surprised at how easily they are able to answer the questions. The answers will be in their notes or direct them to a page and paragraph. This frees you from teaching knowledge based lessons and prepares the students for high level comprehension activities.

The product of the math lesson in Strategy One is notes for the section.

Strategy Three: Keep students motivated

The student-centered style is quite motivating for some students. The students I'm talking about seem to be surprised that they can learn this way, and each day fuels the next. For some it happens right away; others may take a month to six weeks to get hooked on the power of student-centered learning. I try to be a model of a lifelong learner, sharing my interest in puzzles, toys, mazes, kites, geometric art, and anything academic. We build geometric figures with straws for extra credit. I try to make it as fun as I can.

Some students are not highly motivated and tend toward procrastination and socializing rather than doing schoolwork and homework. I would not be honest if I didn't admit that there are some students who refuse to do the work and are way behind schedule. However, the student-centered style leaves these students nowhere to hide. You know who you need help with and who is in danger of failing very early on.

Strategy Four: Make tests a real-time learning experience

Unfortunately, many students are not motivated to learn until there is a test in front of them. All of a sudden they have questions. I capitalize on this opportunity as a learning experience. I let them use the book and I am glad to answer questions during the test. When I correct the test I put small red dots next to the problems they get wrong. I return it to the student to make corrections. Besides being a highly motivating learning experience, it is an opportunity for the student to assess for themselves how much they have learned thus far. They may decide to intensify their work habits. Again, this is another opportunity for creating lifelong learners.

Strategy Five: Grade for learning

It has been argued that the grades in my class are too high. I believe however, that the classroom setting is the place for learning, not a place for pronouncements of success or failure. Standardized Tests are sufficiently appropriate venues for assessing Subject Mastery. Classrooms are for learning.
It is my continued belief and experience that both Subject Mastery and Self Motivational Learning are the keys to success. When we, as Educators, are willing to give the Power and Responsibility for learning back to the student, we will have succeeded. Student Centered Learning is our future.

A secondary math teacher, Paul Bogdan has over 10 years of experience in the classroom, as well as 8 years in the field of computer systems design. He has a BA in Mathematics and a MA in Multidisciplinary Studies. He grew up in Buffalo New York, and has taught in NY, California, and recently got a credential to teach in Oregon.

I am glad to find resources and best practices concerning student-centered learning. I am an Instructional supervisor (I like coach better) at a virtual school working mainly with intervention teachers. We have been focusing on student centered and active learning for some time. In our environment, we must keep the students engaged and focused on their own learning, or they may wander clear out of the classroom! The student centered approach also provides a much needed socialization aspect that many of our students do miss. I love the ideas that I have read on the blog, as I am considering ways to convert them for online learning. I look forward to coming back for more wonderful ideas!

Reading this article has gotten me completely excited to try some new things in my 7th grade math classes. Giving my students the lesson plans to execute will be interesting...although I am sure some students will like this right away, I know I will get some resistance. It was encouraging to read other posters comment that although many will resist right away, just give it time and most or all will come around. I also know that most of my students have very poor note-taking skills, so that will become a priority for me to help them with. The idea of letting the students ask questions during tests (as well as using their books) is something I'll have to think about further. I actually agree with that theory, and have never liked the concept of "grades", but I am not sure of the reaction of fellow teachers/administrators if I made such a drastic change right away. Do you base a student's grade on effort? Or on their standardized tests? Or do you just do away with grades altogether? I am curious about how you handle that part. Any comments?

A student takes a quiz or test when they have completed the classwork and homework. This does not occur at the same moment in time for all students. Students who are conscientious stay on schedule and easily get an A. Students who fall behind fail.

Whether or not 'all or most' of your students stay with the program depends on their motivation to learn.

Math Teacher @ a Project Based Learning Charter High School Brighton, MI

I've found a nice transition into student-centered learning is through setting up learning stations or centers, like the ones found in many pre-school and elementary school classrooms. As a math teacher, I use this for topics where there is more than one way to approach a problem. I will have centers set up around the room, with guided notes/instruction packets to help students understand what I want them to discover at that station. At my school, we have a lot of technology, so I encourage my students to use the Google ChromeBooks to search and discover new mathematical ideas on their own. At the culmination of class, we typically have a discussion about what they learned, what they thought was important/why they thought it was important, and it gives me an opportunity to assess which way my students are learning best.

I found that if you do this often enough, students start to get used to learning on their own and even get excited for it. The first few times, they were a little chatty, but they've gotten much better at it and seem to enjoy "Center Days" now.

I know this is an extremely "late" comment on the topic, but your idea that students don't take the quizzes/tests until they have completed the classwork really interests me. I love that idea and see it as a way to get the kids to realize that the work is part of their opportunity to learn.

My first thought (a negative one, I know) is what do you do with students who don't get the work done by the time the term/semester ends?

Now I understand that my response is coming years after the initial post but I just had to comment on your blog and express my heartfelt appreciation for the information presented. Thank you so much for sharing your evolution as a teacher and for providing some detailed examples of how one can encourage students to take an active role in their own learning. As a former business manager, I understand the importance of inspiring individuals to take an active role in their personal growth and development, therefore I welcome any additional tips or techniques that you have on building a student centered learning environment. Keep up the great work and please continue your gallant effort to convert others to your newfound teaching philosophy.

I had my secondary math methods class read this article, which led to some lively discussion. In your testing method, what are you assessing? Mathematical knowledge or research skills? Exactly how does this motivate your students? How do your students perform on standardized tests? And why are these tests "sufficiently appropriate venues" for assessing?

To them - and myself - this approach seems like simply an alternative to actually teaching your students.